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A modified form of parallel algorithm for solving tridiagonal linear equations is proposed,which is based on the Sherman-Morrison-Woodbury Formula,and suitable for parallel implementation easily.The detail of SMW algorithm is described.This algorithm is compared with DAC(Divide and Conquer) method in both theoretical and practical effect.Both algorithms are tested in parallel machine IBM-SP2 with MPI-C language.The numerical tests show that the speedup and efficiency of DAC method are higher than SMW algorithm.But the communication amount of the latter is very small and SMW algorithm is better than DAC method in numerical stability.